Level B- Grade 3-Operations and Algebraic Thinking
1Standards / 2
Skills Included in Standard / 3
Concepts Included in Standard / 4
Through a Particular Context / 5
Cognitive Demand/ Levels of Thinking / 6
Sample Activity
Operations and Algebraic Thinking
Represent and solve problems involving multiplication and division.
B-3.OA.1
Interpret products of whole numbers, e.g., interpret 5 × 7 as the total number of objects in 5 groups of 7 objects each. For example, describea context in which a total number of objects can be expressed as 5 × 7. / Interpret / products / of whole numbers / Analyzing / Figuring the total number a students needing transportation of a field trip, e.g., 3 classes of 20 each need transportation for the trip
B-3.OA.2
Interpret whole-number quotients of whole numbers, e.g., interpret 56 ÷ 8 as the number of objects in each share when 56 objects are partitioned equally into 8 shares, or as a number of shares when 56 objects are partitioned into equal shares of 8 objects each. Forexample, describe a context in which a number of shares or a number ofgroups can be expressed as 56 ÷ 8. / Interpret / whole-number quotients / of whole numbers / Analyzing / Determining the number of tables and chairs to set up for a party
1
Standards / 2
Skills Included in Standard / 3
Concepts Included in Standard / 4
Through a Particular Context / 5
Cognitive Demand/ Levels of Thinking / 6
Sample Activity
B-3.OA.3
Use multiplication and division within 100 to solve word problems in situations involving equal groups, arrays, and measurement quantities, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem.1 / Use / multiplication and division within 100 / to solve word problems in
situations involving equal groups, arrays, and measurement quantities, / Applying / Figuring the amount of 6-pack sodas to buy for the family reunion, the pounds of lunch meat to buy, the number pizzas to order, based on the number of people being served. How many people can you serve if a serving amount is given along with the total amount of food being bought, etc.?
Also, buying multiples of grocery items (multiplying) or figuring how many can be bought within a certain amount of money (dividing)
B-3.OA.4
Determine the unknown whole number in a multiplication or division equation relating three whole numbers. For example, determine theunknown number that makes the equation true in each of the equations 8× ? = 48, 5 = ?÷ 3, 6 × 6 = ? / Determine / the unknown whole number in a multiplication or division
equation / relating three whole numbers / Analyzing / Set up equations given the three unknowns in reference to planning a party: how many tables seating 4 each will it take to accommodate 64 guests?; how many seats will 4 tables each need to seat all 64 guests?; how many people will fit in a space that has 16 tables that seat 4 people?
1
Standards / 2
Skills Included in Standard / 3
Concepts Included in Standard / 4
Through a Particular Context / 5
Cognitive Demand/ Levels of Thinking / 6
Sample Activity
Understand properties of multiplication and the relationship between multiplication and division.
B-3.OA.5
Apply properties of operations as strategies to multiply and divide.2Examples: If 6 × 4 = 24 is known, then 4 × 6 = 24 is also known. (Commutative property of multiplication.) 3 × 5 × 2 can be found by 3 × 5 = 15, then 15 × 2 = 30, or by 5 × 2 = 10, then 3 × 10 = 30. (Associative property of multiplication.) Knowing that 8 × 5 = 40 and 8 × 2 = 16, one can find 8 × 7 as 8 × (5 + 2) = (8 × 5) + (8 × 2) = 40 + 16 = 56. (Distributive property.) / Apply / Properties of Operations / as strategies to multiply and divide / Apply / Use grocery items such as dozens of eggs, 6, 12 and 24 packs of soft drinks-load items into a refrigerator- if they are arranged 4 across (eggs, 12 or 24 pack) how many rows would there be? Also costs of multiple items- If you buy 8 $5 gifts and 8 $2 gifts, is that the same amount of money as 8 $7 gifts?
B-3.OA.6
Understand division as an unknown-factor problem. For example, find 32 ÷ 8 by finding the number that makes 32 when multiplied by 8. / Understand / Division / as an unknown factor problem / Understand / Divide quantities of food into serving sizes or unit prices- If a serving of roast beef is 4 oz., how many people will a 28 oz. roast serve? If a 4 ounce bottle of sunscreen costs $12 and another brand costs $16 for an 8 ounce bottle, which is the better deal? Why?
1
Standards / 2
Skills Included in Standard / 3
Concepts Included in Standard / 4
Through a Particular Context / 5
Cognitive Demand/ Levels of Thinking / 6
Sample Activity
Multiply and divide within 100.
B-3.OA.7
Fluently multiply and divide within 100, using strategies such as the relationship between multiplication and division (e.g., knowing that 8 × 5 = 40, one knows 40 ÷ 5 = 8) or properties of operations. By the end of Grade 3, know from memory all products of two one-digit numbers. / Multiply and Divide
Know from Memory / within 100
products / using strategies such as the relationship between multiplication and division or properties of operations
two one-digit numbers / Apply
Understand / (See 3.OA 1-6) serving sizes, number of tables at a party, number of soft drinks for a party, etc.
1
Standards / 2
Skills Included in Standard / 3
Concepts Included in Standard / 4
Through a Particular Context / 5
Cognitive Demand/ Levels of Thinking / 6
Sample Activity
Solve problems involving the four operations, and identify and explain patterns in arithmetic.
B-3.OA.8
Solve two-step word problems using the four operations. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding.3 / Solve
Represent
Assess / Two-step Word Problems
Two-step Word
Problems
Reasonableness of answers / Using Four Operations
Using equations with a Letter Standing for Unknown Quantity (variable)
Using Mental Computation and Estimation Strategies (including rounding) / Apply
Apply
Analyze / Have students help create sets of problem cards or power point slides that can be used solo or with partners or small groups in math stations or as daily math questions. For example:
On Monday, Tom’s Bakery had 90 chocolate muffins for sale. 25 chocolate muffins were sold in the morning and 46 in the afternoon. How many chocolate muffins were left?
Gina made a 48 oz. roast beef. Last night, her family ate 16 oz. She wants to makes sandwiches from the leftovers. If she uses 4 oz. per sandwich, how many sandwiches can she make?
Jovan is setting up a conference room. The room needs to seat 120 people. He has 11 tables that will seat 10 people each. Does he have enough tables?
1
Standards / 2
Skills Included in Standard / 3
Concepts Included in Standard / 4
Through a Particular Context / 5
Cognitive Demand/ Levels of Thinking / 6
Sample Activity
B-3.OA.9
Identify arithmetic patterns (including patterns in the addition table or multiplication table), and explain them using properties of operations. For example, observe that 4 times a number is always even, and explainwhy 4 times a number can be decomposed into two equal addends. / Identify
Explain / Arithmetic Patterns
Arithmetic Patterns / Using Properties of Operations
Using Properties of Operations / Understand
Apply / Students can work on Odd or Even Sums/Odd or Even Products then have a group discussion about methods, patterns and the usefulness of the discoveries.
Odd and Even Sums
1. Work with a partner. Investigate whether the sum is even or odd when you add the following:
a) odd number + even number
b) odd number + odd number
c) even number + even number
1.Try at least ten pairs of numbers for each investigation.
2.Explain your findings.
3. When might this information be useful? For example, recently a statistic came out that showed that an odd number of people had gotten married in 2012-why is this strange?
Grade 3- Number and Operations in Base Ten
1Standards / 2
Skills Included in Standard / 3
Concepts Included in Standard / 4
Through a Particular Context / 5
Cognitive Demand/ Levels of Thinking / 6
Sample Activity
Number and Operations in Base Ten
Use place value understanding and properties of operations to perform multi-digit arithmetic.4
B-3.NBT.1
Use place value understanding to round whole numbers to the nearest 10 or 100. / Use / place value understanding to round to the nearest 10 or 100 / whole numbers / Apply / Use dimes and dollars to buy and sell items, groceries, etc. Is the total closer to 60 cents or 70? Is the total closer to $1.00 or $2.00?
B-3.NBT.2
Fluently add and subtract within 1000 using strategies and algorithms based on place value, properties of operations, and/or the relationship between addition and subtraction. / Add
Subtract
Use / within 1000
strategies and algorithms / based on place value, properties of operation and/or the relationship between addition and subtraction / Apply / Have students plan an imaginary event with a budget of $1000. Allow internet use to find the cost of providing music, etc. Have students create PowerPoints of their events.
Have students furnish a room with a budgeted amount. Use local ads for prices.
1
Standards / 2
Skills Included in Standard / 3
Concepts Included in Standard / 4
Through a Particular Context / 5
Cognitive Demand/ Levels of Thinking / 6
Sample Activity
B-3.NBT.3
Multiply one-digit whole numbers by multiples of 10 in the range 10–90 (e.g., 9 × 80, 5 × 60) using strategies based on place value and properties of operations. / Multiply by multiples of 10
Use / whole numbers
strategies / range of 10-90
based on place value and properties of operations. / Apply / Using play money (dimes) or ten-dollar bills, have students buy and sell items in a classroom “store” with set prices of multiples of ten (only allowed to buy a single-digit quantity of items)
Have students note patterns in multiples of ten:
1. All whole number multiples of 10, 100, 1000, etc. end in zero
2. The number of zeroes in a whole number multiple of 10, 100, 1000, etc. is equal to the number of zeros in the multiplier:
72 X 10 = 720 (one zero in ten, one zero in 720)
Use grocery ads advertising 10 for $10, what if you buy 3 of one of the sale items and 7 of another? What if you only buy 7 sale items?
1
Standards / 2
Skills Included in Standard / 3
Concepts Included in Standard / 4
Through a Particular Context / 5
Cognitive Demand/ Levels of Thinking / 6
Sample Activity
Number and Operations- Fractions
Develop understanding of fractions as numbers.
B-3.NF.1
Understand a fraction 1/b as the quantity formed by 1 part when a whole is partitioned into b equal parts; understand a fraction a/b as the quantity formed by a parts of size 1/b. / Understand / that a fraction 1/b as the quantity formed by 1 part when a whole is partitioned into b equal parts; a fraction a/b as the quantity formed by a parts of size 1/b. / when a whole is partitioned into b equal parts / Understand / Use whole objects like pizzas, cakes, yards of fabric, a length of rope or yarn, pieces of wood, pipe or carpet and ask students to partition them physically (cutting or folding). Have students label what each piece represents as a unit fraction (1/b). Then, using the pieces, have students determine the relationship between one piece and the whole, showing the relationship on the board mathematically. Note: Be sure to have students partition into odd and even fractional units (e.g. thirds, fifths as well as halves, fourths, eighths) to demonstrate the variety of fractional units for which this product is applicable.
Grade 3- Number Operations- Fractions
1Standards / 2
Skills Included in Standard / 3
Concepts Included in Standard / 4
Through a Particular Context / 5
Cognitive Demand/ Levels of Thinking / 6
Sample Activity
B-3.NF.3
Explain equivalence of fractions in special cases, and compare fractions by reasoning about their size.
- Understand two fractions as equivalent (equal) if they are the same size, or the same point on a number line.
- Recognize and generate simple equivalent fractions, e.g., 1/2 = 2/4, 4/6 = 2/3). Explain why the fractions are equivalent, e.g., by using a visual fraction model.
- Express whole numbers as fractions, and recognize fractions that are equivalent to whole numbers. Examples: Express 3 in the form3 = 3/1; recognize that 6/1 = 6; locate 4/4 and 1 at the same pointof a number line diagram.
- Compare two fractions with the same numerator or the same denominator by reasoning about their size. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with the symbols >, =, or <, and justify the conclusions, e.g., by using a visual fraction model.
Compare
Understand
Recognize/
generate
Explain
Express
Recognize
Compare
Recognize
Record
Justify / equivalence of fractions
fractions
two fractions as equivalent (equal)
Simple equivalent fractions
Why the fractions are equivalent
whole numbers as fractions
fractions that are equivalent to whole numbers
two fractions with the same numerator or the same denominator
Recognize that comparisons are valid only when the two fractions refer to the same whole
the results of comparisons with the symbols >,=, or <the conclusions / In special cases
by reasoning about their size
if they are the same size, or the same point on a number line
A visual fraction model
Number line diagram
Visual fraction model / Evaluate / Use rulers from 3.NF.2. Have students explore the sizes of the fractional inches with relation to each other. Which is larger, 1/12 or 1/16? Is 4/16 equal to ¼? etc.
The relational size of fractions can also be relayed through discussion of food serving sizes. If two equal -sized pizzas, cakes, etc. are divided into different numbers of servings, which servings are larger?
Grade 3- Measurement and Data
1Standards / 2
Skills Included in Standard / 3
Concepts Included in Standard / 4
Through a Particular Context / 5
Cognitive Demand/ Levels of Thinking / 6
Sample Activity
Measurement and Data
Solve problems involving measurement and estimation of intervals of time, liquid volumes, and masses of objects.
B-3.MD.1
Tell and write time to the nearest minute and measure time intervals in minutes. Solve word problems involving addition and subtraction of time intervals in minutes, e.g., by representing the problem on a number line diagram. / Tell
Write
Measure
Solve / time
time
time intervals
time word problems / to the nearest minute
to the nearest minute
in minutes
addition and subtraction / Apply / Have students use manipulative analog clock, moving the hands to illustrate given times, then show students various times on the clock, having them write the times.
Give starting times for class transitions and ask students how much time has elapsed in minutes.
B-3.MD.2
Measure and estimate liquid volumes and masses of objects using standard units of grams (g), kilograms (kg), and liters (l).6 Add, subtract, multiply, or divide to solve one-step word problems involving masses or volumes that are given in the same units, e.g., by using drawings (such as a beaker with a measurement scale) to represent the problem.7 / Measure
Estimate / liquid volumes / using standard (metric) units / Understand / Have various objects for students to estimate their mass and volume and have students measure and make a chart of estimations and actual measurements. Based on measurements of small portable items (a jar of pickles), have students estimate the mass and volume of a barrel of pickles.
This can be useful in a discussion of buying items at warehouse type stores, Costco, Sam’s Club, etc. An extension topic can be determining which is cheaper to buy per volume unit, a small jar of pickles or a giant one?
1
Standards / 2
Skills Included in Standard / 3
Concepts Included in Standard / 4
Through a Particular Context / 5
Cognitive Demand/ Levels of Thinking / 6
Sample Activity
Represent and interpret data.
B-3.MD.3
Draw a scaled picture graph and a scaled bar graph to represent a data set with several categories. Solve one- and two-step “how many more” and “how many less” problems using information presented in scaled bar graphs. For example, draw a bar graph in which each square inthe bar graph might represent 5 pets. / Draw
Solve / scaled picture graph and scaled bar graph
one-and two-step “how many more” and “how many less” problems / using information presented in scaled graphs / Apply / Have students create scaled graphs (picture and bar) by polling their classmates (favorite color, number of pets, etc.) Students will create the graph, then discuss questions such as “Who has the greatest number of pets? How many more people like blue than red?”
B-3.MD.4
Generate measurement data by measuring lengths using rulers marked with halves and fourths of an inch. Show the data by making a line plot, where the horizontal scale is marked off in appropriate units— whole numbers, halves, or quarters. / Generate
Show / measurement data / measuring lengths using rulers marked with ½’s and ¼’s of an inch.
marking line plot with appropriately marked horizontal scale / Apply / Have students measure their heights to the nearest ¼ inch and post on an appropriately scaled number line/ruler.
1
Standards / 2
Skills Included in Standard / 3
Concepts Included in Standard / 4
Through a Particular Context / 5
Cognitive Demand/ Levels of Thinking / 6
Sample Activity
Geometric measurement: understand concepts of area and relate area to multiplication and to addition.
B-3.MD.5
Recognize area as an attribute of plane figures and understand concepts of area measurement.
- A square with side length 1 unit, called “a unit square,” is said to have “one square unit” of area, and can be used to measure area.
- A plane figure which can be covered without gaps or overlaps by n unit squares is said to have an area of n square units.
Understand / Area as an attribute
concepts
(a)unit square, one square unit
(b)(n unit squares, n square units) / plane figures
area measurement / Understand / Use unit squares of various sizes to measure planes in the classroom: desk tops, the blackboard or white board. Use unit squares such as Cheezits to measure the area of a plate, etc.
Discuss the way in which floor coverings are sold (by the square unit). How many square feet of tile would be needed to redo the classroom floor? A 12X12 piece of scrapbook paper can be used for students to try by discovery as a scaffold to the formula.
B-3.MD.6
Measure areas by counting unit squares (square cm, square m, square in, square ft, and improvised units). / Measure / areas / counting unit squares / Understand / Continuing from 3.MD.5, have students measure areas by counting unit squares, this can also be accomplished using graph paper or-teacher-generated arrays.
1
Standards / 2
Skills Included in Standard / 3
Concepts Included in Standard / 4
Through a Particular Context / 5
Cognitive Demand/ Levels of Thinking / 6
Sample Activity
B-3.MD.7
Relate area to the operations of multiplication and addition.
- Find the area of a rectangle with whole-number side lengths by tiling it, and show that the area is the same as would be found by multiplying the side lengths.
- Multiply side lengths to find areas of rectangles with whole number side lengths in the context of solving real world and mathematical problems, and represent whole-number products as rectangular areas in mathematical reasoning.
- Use tiling to show in a concrete case that the area of a rectangle with whole-number side lengths a and b + c is the sum of a × b and a × c. Use area models to represent the distributive property in mathematical reasoning.
- Recognize area as additive. Find areas of rectilinear figures by decomposing them into non-overlapping rectangles and adding the areas of the non-overlapping parts, applying this technique to solve real world problems.